New paper digests OpenAI's Haldane-gap proof with tensor networks, formalizes it in Lean 4
danintheory · x · 2026-11-11
A new arXiv paper by Sirui Lu, Bridging Gaps with Tensor Networks: From the Haldane Gap and Beyond, verifies, digests, and formalizes OpenAI's computer-assisted proof of a uniform gap in the periodic spin-1 Heisenberg chain.
- Tensor-network diagrams read the partition-function network along space and imaginary time, showing how finite-ring bounds propagate across doubled lengths and inverse temperatures
- The spin-1 bound is sharpened by a factor of 19 from the same finite inputs, yielding ΔL > 0.0729 for all even L ≥ 36
- Reflection positivity is identified as the general condition behind the proof, and uniform gaps are certified in seven additional spin chains and ladders
- All theorems are formalized in Lean 4, with code and certificates publicly available
The author argues that digesting machine-generated proofs into transparent physical mechanisms yields sharper bounds, broader theorems, and reusable formal verifications.
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